aA THEORY OF STATISTICS. 
Twelve Dice thrown 4096 times, a throw of 4, 5, or 6 points re-koned 
a success (p. 258). 
Expected 
Observed P 
No. of Frequency ’ (m' —m)? 
Successes. F a (m) (m' =m) zon 
i 4096(% +3)12 
0 0 1 1 1°0000 
! 7 12 25 2°0833 
60 66 | 36 5455 
198 220 484 2°2000 
430 495 4225 85354 
731 792 3721 4:6982 
948 924 576 ‘6234 
847 792 3025 38194 
536 495 1681 3°3960 
257 220 1369 6:2227 
1 71 66 25 ‘3788 
11 12 i 0833 
12 0 1 1°0000 
Totals £396 23 ed 34:5860 = y* 
From the tables we find :— 
n'. x. 2. 
13 30 1002792 
13 40 ‘000072 
Hence, by interpolation for x2=34'5860, P="0015. 
Twelve Dice thrown 4096 times, a throw of 6 points reckoned a success. 
Expected 
No. of el Frequency / 2 (m' =m)? 
Frequency (m' —m)% ye iy 
Successes. (m) (m) m 
: 4096(% + #)'2 
n 447 459 144 3137 
1145 1103 1764 15993 
1181 1213 1024 8442 
796 809 x 169 2089 
380 364 256 7033 
115 116 11 *0086 
24 27 J) *3333 
7 and over 8] 5 9 1:8000 
Totals 3 3 a 58113 =" 
From the tables we find :— 
n', x> 2 
8 5 '659963 
8 6 539750 
Henee, by interpolation for x2=5'8113, P= 5624. 
5 Ps 
at 409r 
409% 409¢